Open Access
2010 (α,β)-fuzzy Lie algebras over an (α,β)-fuzzy field
P. L. Antony, P. L. Lilly
J. Gen. Lie Theory Appl. 4: 1-8 (2010). DOI: 10.4303/jglta/G090701
Abstract

The concept of (α,β)-fuzzy Lie algebras over an (α,β)-fuzzy field is introduced. We provide characterizations of an $(\in,\in\vee q)$-fuzzy Lie algebra over an $(\in,\in\vee q)$-fuzzy field.

References

1.

M. Akram. Generalized fuzzy Lie subalgebra. J. Gen. Lie Theory Appl., 2 (2008), 261–268. MR2476784 1184.17014 10.4303/jglta/S070401 M. Akram. Generalized fuzzy Lie subalgebra. J. Gen. Lie Theory Appl., 2 (2008), 261–268. MR2476784 1184.17014 10.4303/jglta/S070401

2.

M. Akram and W. A. Dudek. Generalized fuzzy subquasigroups. Quasigroups Related Systems, 16 (2008), 133–146. MR2494872 1178.20060 M. Akram and W. A. Dudek. Generalized fuzzy subquasigroups. Quasigroups Related Systems, 16 (2008), 133–146. MR2494872 1178.20060

3.

P. L. Antony and P. L. Lilly. Some properties of fuzzy Lie algebra over fuzzy field. Accepted for Publication in Proceedings of the International Seminar on Topology and Applications, 19-21 March 2009, CRMS, St.Joseph's College, Irinjalakuda, India. MR2645322 1203.17015 10.4303/jglta/S090701 P. L. Antony and P. L. Lilly. Some properties of fuzzy Lie algebra over fuzzy field. Accepted for Publication in Proceedings of the International Seminar on Topology and Applications, 19-21 March 2009, CRMS, St.Joseph's College, Irinjalakuda, India. MR2645322 1203.17015 10.4303/jglta/S090701

4.

S. K. Bhakat and P. Das. Fuzzy subrings and ideals redefined. Fuzzy Sets and Systems, 81 (1996), 383–393. MR1401664 10.1016/0165-0114(95)00202-2 0878.16025 S. K. Bhakat and P. Das. Fuzzy subrings and ideals redefined. Fuzzy Sets and Systems, 81 (1996), 383–393. MR1401664 10.1016/0165-0114(95)00202-2 0878.16025

5.

L. Guangwen and G. Enrui. Fuzzy algebras and fuzzy quotient algebras over fuzzy fields.Electronic Busefal, 85 (2001), 1–4. L. Guangwen and G. Enrui. Fuzzy algebras and fuzzy quotient algebras over fuzzy fields.Electronic Busefal, 85 (2001), 1–4.

6.

G. J. Klir and B. Yuan. Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall PTR, New Jersey, 2006. MR1329731 0915.03001 G. J. Klir and B. Yuan. Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall PTR, New Jersey, 2006. MR1329731 0915.03001

7.

J. E. Humphreys. Introduction to Lie Algebra and Representation Theory. Springer-Verlag, New York, 1972. MR323842 J. E. Humphreys. Introduction to Lie Algebra and Representation Theory. Springer-Verlag, New York, 1972. MR323842

8.

D. S. Malik and J. N. Mordeson. Fuzzy vector spaces. Inform. Sci., 55 (1991), 271–281. MR1080457 10.1016/0020-0255(91)90018-P 0727.15001 D. S. Malik and J. N. Mordeson. Fuzzy vector spaces. Inform. Sci., 55 (1991), 271–281. MR1080457 10.1016/0020-0255(91)90018-P 0727.15001

9.

S. Nanda. Fuzzy algebras over fuzzy fields. Fuzzy Sets and Systems, 37 (1990), 99–103. MR1069610 10.1016/0165-0114(90)90067-G 0703.16025 S. Nanda. Fuzzy algebras over fuzzy fields. Fuzzy Sets and Systems, 37 (1990), 99–103. MR1069610 10.1016/0165-0114(90)90067-G 0703.16025

10.

B. M. Pu and Y. M. Liu. Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence. J. Math. Anal. Appl., 76 (1980), 571–599. MR587361 0447.54006 10.1016/0022-247X(80)90048-7 B. M. Pu and Y. M. Liu. Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence. J. Math. Anal. Appl., 76 (1980), 571–599. MR587361 0447.54006 10.1016/0022-247X(80)90048-7

11.

S. E. Yehia. Fuzzy ideals and fuzzy subalgebras of Lie algebras. Fuzzy Sets and Systems, 80 (1996), 237–244. MR1390863 10.1016/0165-0114(95)00109-3 0874.17032 S. E. Yehia. Fuzzy ideals and fuzzy subalgebras of Lie algebras. Fuzzy Sets and Systems, 80 (1996), 237–244. MR1390863 10.1016/0165-0114(95)00109-3 0874.17032

12.

L. A. Zadeh. Fuzzy sets. Information and Control, 8 (1965), 338–353. } MR219427 L. A. Zadeh. Fuzzy sets. Information and Control, 8 (1965), 338–353. } MR219427
Copyright © 2010 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)
P. L. Antony and P. L. Lilly "(α,β)-fuzzy Lie algebras over an (α,β)-fuzzy field," Journal of Generalized Lie Theory and Applications 4(none), 1-8, (2010). https://doi.org/10.4303/jglta/G090701
Published: 2010
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